Passages from
How Math Works
In mathematics, by placing our fingers on a given problem, no matter how trite or pedestrian it apparently seems, we may end up measuring the pulse of the universe.
— How Math Works, p. 119
It is almost as if ideas set in mathematical form melt and become liquid and just as rivers can, from the most humble beginnings, flow for thousands of miles, through the most varied topography bringing nourishment and life with them wherever they go,
so too can ideas cast in mathematical form flow far from their original sources, along well-defined paths, electrifying and dramatically affecting much of what they touch.
— How Math Works, pp. xii - xiii
A goal of this book has been to tear down in some small part these barriers to understanding by attempting to shatter the “divinity of arithmetic,”
through showing that even the methods, which we now take most for granted, were not given to us from on high, but were actually the result of centuries of scientific efforts on the part of our predecessors.
— How Math Works, p. 269
Through the judicious employment of symbols, diagrams, and calculations, mathematics enables us to acquire significant facts about extremely significant things (universal laws, even),
not by first forging out into the cosmos with teams of scientists, but rather from the comforts and confines of coffee tables in our living rooms!
— How Math Works, p. 72
Awareness of the fact that one thing in nature can be substituted for another in a crushingly advantageous way is what enabled Eratosthenes to do this.
The key point being that while we as humans do discriminate between forms, a small circle in the dirt as being something drastically different from a large one that goes around the earth, many of the fundamental rules that we learn about them do not.
A circle is a circle is a circle and once the essential laws have been obtained wherever that is, they apply across the spectrum of forms, from a small circle drawn in the dirt more than 4,000 years ago to a modern circle as large as the very earth itself. It simply makes no difference.
— How Math Works, p. 70
Throughout what follows, the often-mentioned computational efficiency of the Hindu-Arabic notation will be on full display. However, there is also much “conceptual manna” to be gleaned from the coin numeral and abacus models that we have developed.
So instead of tossing these systems aside as interesting curiosities and forgetting about them, we will now recalibrate them to become potent weapons of exposition.
These models then will comprise a crucial portion of the conceptual arsenal which we will employ full force in our efforts to give readers a newfound appreciation for the elementary arithmetic already in their possession.
— How Math Works, p. 72